Data from 1960 to 2010 raining days, there are 4168 observations 13 days of which are rain exceeds 1000 (10cm)
Change of exceeds 1000 is 0.003119002 0.31% change
library(tidyverse)
library(readr)
library(drc)
library(reshape2)
#install.packages("moments")
library("moments") # for skewness of data
Data
read.csv("./raw/prcp.csv") %>%
mutate(date = as.Date(date)) %>%
mutate(year = format(date, "%Y")) %>%
filter(prcp != 0) %>%
dplyr::select(date, year, prcp) -> data
data %>%
filter(year <= 2020) %>%
pull(prcp) %>%
hist(breaks = 1000, plot = FALSE) -> hist
Modling Distribution
Use data from 1960 - 2010 for modeling precipitation
hist$counts %>% sum() -> sum
x <- hist$mids
y <- hist$counts/sum
data.frame(x, y) -> dens
summary(model)
Model fitted: Exponential decay with lower limit at 0 (2 parms)
Parameter estimates:
Estimate Std. Error t-value p-value
d:(Intercept) 0.1407885 0.0012481 112.80 < 2.2e-16 ***
e:(Intercept) 1.3292414 0.0077504 171.51 < 2.2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error:
0.001397153 (945 degrees of freedom)
plot(x = dens$x, y = fitted(model), type = "l", col = "blue", xlim = c(0, 300))
lines(x = dens$x, y = dens$y, type = "p", col = alpha("black", 0.5))

mod.exd <- drm(y ~ x, fct = EXD.2(), data = dens)
plot(x = dens$x, y = fitted(mod.exd), type = "l", col = "blue", xlim = c(0,300))
lines(x = dens$x, y = dens$y, type = "p", col = alpha("black", 0.5))

summary(mod.exd)
Model fitted: Exponential decay with lower limit at 0 (2 parms)
Parameter estimates:
Estimate Std. Error t-value p-value
d:(Intercept) 0.1167687 0.0021435 54.476 < 2.2e-16 ***
e:(Intercept) 9.3269006 0.2794558 33.375 < 2.2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error:
0.00182667 (945 degrees of freedom)
1 - pexp(log(1000)*k, d)
[1] 0.005534439
1/d
[1] 7.102853
data %>%
filter(year <= 2010) %>%
pull(prcp) %>%
mean() %>%
log()*k
[1] 23.28785
0.31% change versus 0.442%
Labs:
A Single Years 20 year roll
yr = 1960
data %>%
filter((year >= yr) & (year <= yr + 9)) %>%
pull(prcp) %>%
hist(breaks = 1000, plot = FALSE) -> hist
hist$counts %>% sum() -> sum
x <- hist$mids
y <- hist$counts/sum
data.frame(x, y) -> dens
mod <- drm(data = dens, y ~ log(x), fct = EXD.2())
d <- mod$parmMat[1]
e <- mod$parmMat[2]
k <- 1/e/d
1 - pexp(log(1000)*k, d)
[1] 0.0002201357
plot(x = dens$x, y = fitted(mod), type = "l", col = "blue", xlim = c(0, 300))
lines(x = dens$x, y = dens$y, type = "p", col = alpha("black", 0.5))

yr = 1970
data %>%
filter((year >= yr) & (year <= yr + 9)) %>%
pull(prcp) %>%
hist(breaks = 1000, plot = FALSE) -> hist
hist$counts %>% sum() -> sum
x <- hist$mids
y <- hist$counts/sum
data.frame(x, y) -> dens
mod <- drm(data = dens, y ~ log(x), fct = EXD.2())
d <- mod$parmMat[1]
e <- mod$parmMat[2]
k <- 1/e/d
1 - pexp(log(1000)*k, d)
[1] 0.002985969
plot(x = dens$x, y = fitted(mod), type = "l", col = "blue", xlim = c(0, 300))
lines(x = dens$x, y = dens$y, type = "p", col = alpha("black", 0.5))

1 - pexp(log(1000)*k, d)
[1] 0.00457532
mean = 76.84094 sd = 144.0488
Explonential Explainability

Risk Trends
Risks Through out Years
mtr <- data.frame(year = YEAR)
list <- c()
for (i in YEAR){
data %>%
filter((year >= i) & (year <= i + 9)) %>%
pull(prcp) %>%
hist(breaks = 400, plot = FALSE) -> hist
hist$counts %>% sum() -> sum
x <- hist$mids
y <- hist$counts/sum
data.frame(x, y) -> dens
mod <- drm(data = dens, y ~ log(x), fct = EXD.2())
d <- mod$parmMat[1]
e <- mod$parmMat[2]
k <- 1/e/d
p <- 1 - pexp(log(1000)*k, d)
list <- c(list, p)
}
NaNs producedNaNs producedNaNs produced
plot(1:length(list), list)

Use smaller breaks
Find the right break numbers
YEAR <- c(1960, 1980, 2000)
BREAKS <- c(19, 20, 21, 22)
lenlist <- c()
kulist <- c()
for(yr in YEAR){
data %>%
filter((year >= yr) & (year <= yr + 19)) %>%
dplyr::select(year, prcp) %>%
pull(prcp) %>%
length() -> n
lenlist <- c(lenlist, n)
data %>%
filter((year >= yr) & (year <= yr + 19)) %>%
dplyr::select(year, prcp) %>%
pull(prcp) %>%
kurtosis() -> ku
kulist <- c(kulist, ku)
}
Square_root = c()
Sturges = c()
Rice = c()
Donna = c()
for(n in lenlist){
sq = ceiling(n^0.5)
sg = ceiling(log(n, 2)) + 1
rc = ceiling(2*n^(1/3))
igh = (6*(n - 2)/(n +1)/(n +3))^0.5
dn = log(abs(1 + kulist[which(lenlist %in% n)]/igh) , 2) + log(n, 2) + 1
Square_root = c(Square_root, sq)
Sturges = c(Sturges, sg)
Rice = c(Rice, rc)
Donna = c(Donna, dn)
}
data.frame( Year = YEAR,
Length = lenlist,
Square_root = Square_root,
Sturges = Sturges,
Rice = Rice,
Donna = Donna
) -> meth
meth
Work Flow
In a 10 years interval compute risks of precipitation higher than 10cm (prcp > 1000) by using different breaks of histogram from usgin 250 to 1000
Choosing bin have many choices actually
YEAR <- c(1960, 1980, 2000)
BREAKS <- c(19, 20, 21, 22, 30, 40, 50, 60, 70, 80, 90)
for(n in BREAKS)
data %>%
filter((year >= 1960) & (year <= 1969)) %>%
pull(prcp) %>%
hist(breaks = n)











kurtosis(data$prcp)
[1] 31.3595
list <- c()
listB <- c()
Year <- c()
dlist <- c()
elist <- c()
klist <- c()
for(n in BREAKS){
for(i in YEAR){
data %>%
filter((year >= i) & (year <= i + 19)) %>%
pull(prcp) %>%
hist(breaks = n, plot = FALSE) -> hist
hist$counts %>% sum() -> sum
x <- hist$mids
y <- hist$density
data.frame(x, y) -> dens
mod <- drm(data = dens, y ~ log(x), fct = EXD.2())
d <- mod$parmMat[1]
e <- mod$parmMat[2]
k <- 1/e/d
p <- 1 - pexp(log(1500)*k, d)
list <- c(list, p)
listB <- c(listB, n)
Year <- c(Year, i)
dlist <- c(dlist, d)
elist <- c(elist, e)
klist <- c(klist, k)
}}
mtr <- data.frame(year = Year,
Breaks = listB,
Probability = list,
parameter_d = dlist,
parameter_e = elist,
parameter_k = klist)
Visulisation
ggplotly(g)
n too large, allowed maximum for palette Blues is 9
Returning the palette you asked for with that many colors
mtr %>%
mutate(year = as.factor(year)) %>%
mutate(Breaks = as.factor(Breaks)) %>%
ggplot(aes(y = parameter_d, x = parameter_e, color = year)) +
geom_jitter(alpha = 0.8) +
scale_color_brewer(palette = "Reds") +
theme(panel.border = element_blank(),
panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
panel.background = element_rect(fill = "#fafafa"),
plot.background = element_rect(fill = "white")
) +
xlab("parameter e: skewness of the curve") +
ylab("parameter d: height of the curve")
Parameter d influence the height of pdf, parameter e influence the lenghth of pdf… this suggest in general, precipitation distribution cure are getting flatter and
plot_ly(x= mtr$parameter_e, y= mtr$parameter_d, z=mtr$Breaks, type="scatter3d", mode="markers", color=mtr$year)
mtr %>%
dplyr::select(year, Breaks, parameter_d, parameter_e) %>%
mutate(Breaks = as.factor(Breaks)) %>%
melt(id = c("year", "Breaks"), variable.name = "parameter") %>%
ggplot(aes(x = year, y = value)) +
geom_line(aes(x = year, y = value, linetype = parameter, color = Breaks)) +
scale_color_brewer(palette = "Purples") +
theme(panel.border = element_blank(),
panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
panel.background = element_rect(fill = "#fafafa"),
plot.background = element_rect(fill = "white")
)
mtr %>%
mutate(Breaks = as.factor(Breaks)) %>%
ggplot(aes(x = year, y = parameter_k, color = Breaks)) +
geom_point() +
geom_line() +
scale_color_brewer(palette = "Blues") +
theme(panel.border = element_blank(),
panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
panel.background = element_rect(fill = "#fafafa"),
plot.background = element_rect(fill = "white")
)
calculate different
list <- c()
listB <- c()
Year <- c()
dlist <- c()
elist <- c()
for(n in BREAKS){
for(i in YEAR){
data %>%
filter((year >= i) & (year <= i + 9)) %>%
pull(prcp) %>%
hist(breaks = n, plot = FALSE) -> hist
hist$counts %>% sum() -> sum
x <- hist$mids
y <- hist$counts/sum
data.frame(x, y) -> dens
mod <- drm(data = dens, y ~ log(x), fct = EXD.2())
d <- mod$parmMat[1]
e <- mod$parmMat[2]
k <- 1/e/d
p <- 1 - pexp(log(600)*k, d)
list <- c(list, p)
listB <- c(listB, n)
Year <- c(Year, i)
dlist <- c(dlist, d)
elist <- c(elist, e)
}}
mtr <- data.frame(year = Year,
Breaks = listB,
Probability = list,
parameter_d = dlist,
parameter_e = elist)
mtr %>%
mutate(Breaks = as.factor(Breaks)) %>%
ggplot(aes(x = year, y = Probability, color = Breaks)) +
geom_point() +
geom_line() +
scale_color_brewer(palette = "Blues") +
theme(panel.border = element_blank(),
panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
panel.background = element_rect(fill = "#fafafa"),
plot.background = element_rect(fill = "white")
)
g <- df %>%
ggplot(aes(x = date, y = prcp)) +
geom_line(color = "blue") +
theme(panel.border = element_blank(),
panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
panel.background = element_rect(fill = "#fafafa"),
plot.background = element_rect(fill = "white")
) +
geom_line(aes(x = date, y = rep(1500, length(date))), color = "lightblue") +
ylab("Precipitation (in tenth of mm")
ggplotly(g)
data %>%
filter(prcp >= 1000)
mtr %>%
filter(Breaks == 21) %>%
left_join(meth, by = c("year" = "Year")) %>%
select(year, Probability, Length) %>%
mutate(days = Probability*Length)
---
title: "R Notebook"
output: html_notebook
editor_options: 
  chunk_output_type: inline
---

Data from 1960 to 2010 raining days, there are 4168 observations 13 days of which are rain exceeds 1000 (10cm)

Change of exceeds 1000 is 0.003119002 0.31% change

```{r}

library(tidyverse)
library(readr)
library(drc)
library(reshape2)

#install.packages("moments")                
library("moments") # for skewness of data
```

# Data

```{r}
read.csv("./raw/prcp.csv") %>%
  mutate(date = as.Date(date)) %>%
  mutate(year = format(date, "%Y")) %>%
  filter(prcp != 0) %>%
  dplyr::select(date, year, prcp) -> data

data %>%
  filter(year <= 2020) %>%
  pull(prcp) %>%
  hist(breaks = 1000, plot = FALSE) -> hist
```

# Modling Distribution

Use data from 1960 - 2010 for modeling precipitation

```{r}
hist$counts %>% sum() -> sum
x <- hist$mids 
y <- hist$counts/sum 

data.frame(x, y) -> dens 
```

```{r}
model <- drm(data = dens, y ~ log(x), fct = EXD.2())
summary(model)
d = 0.1407885
e = 1.3292414

k <- 1/e/d
```

```{r}
plot(x = dens$x, y = fitted(model), type = "l", col = "blue", xlim = c(0, 300))
lines(x = dens$x, y = dens$y, type = "p", col = alpha("black", 0.5))
```

```{r}
mod.exd <- drm(y ~ x, fct = EXD.2(), data = dens)
```

```{r}
plot(x = dens$x, y = fitted(mod.exd), type = "l", col = "blue", xlim = c(0,300))
lines(x = dens$x, y = dens$y, type = "p", col = alpha("black", 0.5))
```

```{r}
summary(mod.exd)
```

```{r}
1 - pexp(log(1000)*k, d)

1/d

data %>%
  filter(year <= 2010) %>%
  pull(prcp) %>%
  mean() %>%
  log()*k
```

0.31% change versus 0.442%

# Labs:

## A Single Years 20 year roll

```{r}
yr = 1960
data %>%
  filter((year >= yr) & (year <= yr + 9)) %>%
  pull(prcp) %>%
  hist(breaks = 1000, plot = FALSE) -> hist
hist$counts %>% sum() -> sum
x <- hist$mids 
y <- hist$counts/sum 
data.frame(x, y) -> dens 
mod <- drm(data = dens, y ~ log(x), fct = EXD.2())
d <- mod$parmMat[1]
e <- mod$parmMat[2]
k <- 1/e/d
1 - pexp(log(1000)*k, d)

plot(x = dens$x, y = fitted(mod), type = "l", col = "blue", xlim = c(0, 300))
lines(x = dens$x, y = dens$y, type = "p", col = alpha("black", 0.5))
```

```{r}
yr = 1970
data %>%
  filter((year >= yr) & (year <= yr + 9)) %>%
  pull(prcp) %>%
  hist(breaks = 1000, plot = FALSE) -> hist
hist$counts %>% sum() -> sum
x <- hist$mids 
y <- hist$counts/sum 
data.frame(x, y) -> dens 
mod <- drm(data = dens, y ~ log(x), fct = EXD.2())
d <- mod$parmMat[1]
e <- mod$parmMat[2]
k <- 1/e/d
1 - pexp(log(1000)*k, d)

plot(x = dens$x, y = fitted(mod), type = "l", col = "blue", xlim = c(0, 300))
lines(x = dens$x, y = dens$y, type = "p", col = alpha("black", 0.5))
```

```{r}
yr = 1980
data %>%
  filter((year >= yr) & (year <= yr + 9)) %>%
  pull(prcp) %>%
  hist(breaks = 1000, plot = FALSE) -> hist
hist$counts %>% sum() -> sum
x <- hist$mids 
y <- hist$density 
data.frame(x, y) -> dens 
mod <- drm(data = dens, y ~ log(x), fct = EXD.2())
d <- mod$parmMat[1]
e <- mod$parmMat[2]
k <- 1/e/d
1 - pexp(log(1000)*k, d)

data %>%
  filter((year >= yr) & (year <= yr + 9)) %>%
  mutate(trans = log(prcp)*k)
```
mean = 76.84094
sd = 144.0488

## Explonential Explainability
```{r}
data %>%
  pull(prcp) %>%
  hist(breaks = 1000, plot = FALSE) -> hist
hist$counts %>% sum() -> sum
x <- hist$mids 
y <- hist$density 
data.frame(x, y) -> dens 
mod <- drm(data = dens, y ~ log(x), fct = EXD.2())
d <- mod$parmMat[1]
e <- mod$parmMat[2]
k <- 1/e/d

# just verify the function we use worked
ggplot(data.frame(x, y), aes(x, y)) + geom_point() + geom_function(fun = ~ d*exp(-log(.x)/e), color = "red") + geom_line(data = data.frame(x, fitted(mod)), aes(x, fitted.mod.), color = 'blue')

# fitted function (red) + fited value (blue)
ggplot(data.frame(x, y), aes(x, y)) + geom_point() + geom_function(fun = ~ d*exp(-d*log(.x)*k), color = "red") + geom_line(data = data.frame(x, fitted(mod)), aes(x, fitted.mod.), color = 'blue')

ggplot(data.frame(x, y), aes(x, y)) + geom_point() + geom_function(fun = ~ d*exp(-d*log(.x)*k), color = "red") + geom_line(data = data.frame(x, fitted(mod)), aes(x, fitted.mod.), color = 'blue')

ggplot(data.frame(x, y), aes(x, y)) + geom_point() + geom_function(fun = ~ d*exp(-d*log(.x)*k), color = "red") + geom_line(data = data.frame(x, fitted(mod)), aes(x, fitted.mod.), color = 'blue')

```


## Risk Trends

## Risks Through out Years

```{r}
mtr <- data.frame(year = YEAR)
list <- c()

for (i in YEAR){
    data %>%
      filter((year >= i) & (year <= i + 9)) %>%
      pull(prcp) %>%
      hist(breaks = 400, plot = FALSE) -> hist
    hist$counts %>% sum() -> sum
    x <- hist$mids 
    y <- hist$counts/sum 
    data.frame(x, y) -> dens 
    mod <- drm(data = dens, y ~ log(x), fct = EXD.2())
    d <- mod$parmMat[1]
    e <- mod$parmMat[2]
    k <- 1/e/d
    p <- 1 - pexp(log(1000)*k, d)
    list <- c(list, p)
}
plot(1:length(list), list)
```

```{r}

```

## Use smaller breaks

Find the right break numbers

```{r}
YEAR <- c(1960, 1980, 2000)
BREAKS <- c(19, 20, 21, 22)
```

```{r}
lenlist <- c()
kulist <- c()
for(yr in YEAR){
data %>%
      filter((year >= yr) & (year <= yr + 19)) %>%
      dplyr::select(year, prcp) %>% 
      pull(prcp) %>%
      length() -> n
  lenlist <- c(lenlist, n)
data %>%
      filter((year >= yr) & (year <= yr + 19)) %>%
      dplyr::select(year, prcp) %>% 
      pull(prcp) %>%
      kurtosis() -> ku
  kulist <- c(kulist, ku)
}
Square_root = c()
Sturges = c()
Rice = c()
Donna = c()
for(n in lenlist){
  sq = ceiling(n^0.5)
  sg = ceiling(log(n, 2)) + 1
  rc = ceiling(2*n^(1/3))
  igh = (6*(n - 2)/(n +1)/(n +3))^0.5
  dn = log(abs(1 + kulist[which(lenlist %in% n)]/igh) , 2) + log(n, 2) + 1
Square_root = c(Square_root, sq)
Sturges = c(Sturges, sg)
Rice = c(Rice, rc)
Donna = c(Donna, dn)
}
data.frame( Year = YEAR,
          Length = lenlist,
           Square_root = Square_root, 
           Sturges = Sturges,
           Rice = Rice, 
           Donna = Donna
           ) -> meth
```

```{r}
meth
```

# Work Flow

In a 10 years interval compute risks of precipitation higher than 10cm (prcp \> 1000) by using different breaks of histogram from usgin 250 to 1000

Choosing bin have many choices actually

```{r}
YEAR <- c(1960, 1980, 2000)
BREAKS <- c(19, 20, 21, 22, 30, 40, 50, 60, 70, 80, 90)
```

```{r}
for(n in BREAKS)
  data %>%
      filter((year >= 1960) & (year <= 1969)) %>%
      pull(prcp) %>%
      hist(breaks = n)
```

```{r}
kurtosis(data$prcp)
```

```{r}
list <- c()
listB <- c()
Year <- c()
dlist <- c()
elist <- c()
klist <- c()
for(n in BREAKS){
  for(i in YEAR){
    data %>%
      filter((year >= i) & (year <= i + 19)) %>%
      pull(prcp) %>%
      hist(breaks = n, plot = FALSE) -> hist
    hist$counts %>% sum() -> sum
    x <- hist$mids 
    y <- hist$density 
    data.frame(x, y) -> dens 
    mod <- drm(data = dens, y ~ log(x), fct = EXD.2())
    d <- mod$parmMat[1]
    e <- mod$parmMat[2]
    k <- 1/e/d
    p <- 1 - pexp(log(1500)*k, d)
    list <- c(list, p)
    listB <- c(listB, n)
    Year <- c(Year, i)
    dlist <- c(dlist, d)
    elist <- c(elist, e)
    klist <- c(klist, k)
  }}
mtr <- data.frame(year = Year,
                    Breaks = listB, 
                      Probability = list, 
                  parameter_d = dlist,
                  parameter_e = elist,
                  parameter_k = klist)
```

# Visulisation

```{r}
library(wesanderson)
mtr %>%
  mutate(Breaks = as.factor(Breaks)) %>%
  ggplot(aes(x = year, y = Probability, color = Breaks)) + 
    geom_point() + 
    geom_line() + 
    scale_color_brewer(palette = "Blues") +
  theme(panel.border = element_blank(),
          panel.grid.major = element_blank(),
          panel.grid.minor = element_blank(),
          panel.background = element_rect(fill = "#fafafa"),
          plot.background = element_rect(fill = "white")
        ) + 
    ylab("Risks of Rain Exceeds 10cm") + 
    ggtitle("Risks of Rain Exceeding 15 cm increase evey 2 decades") +
    xlab("Two Decades Time From _ ") -> g
library(plotly)
ggplotly(g)
```

```{r}
mtr %>%
  mutate(year = as.factor(year)) %>%
  mutate(Breaks = as.factor(Breaks)) %>%
  ggplot(aes(y = parameter_d, x = parameter_e, color = year)) + 
    geom_jitter(alpha = 0.8) + 
    scale_color_brewer(palette = "Reds") +
  theme(panel.border = element_blank(),
          panel.grid.major = element_blank(),
          panel.grid.minor = element_blank(),
          panel.background = element_rect(fill = "#fafafa"),
          plot.background = element_rect(fill = "white")
        ) + 
    xlab("parameter e: skewness of the curve") + 
    ylab("parameter d: height of the curve") 
    
```

Parameter d influence the height of pdf, parameter e influence the lenghth of pdf... this suggest in general, precipitation distribution cure are getting flatter and

```{r}
plot_ly(x= mtr$parameter_e, y= mtr$parameter_d, z=mtr$Breaks, type="scatter3d", mode="markers", color=mtr$year)
```

```{r}
mtr %>%
  dplyr::select(year, Breaks, parameter_d, parameter_e) %>%
  mutate(Breaks = as.factor(Breaks)) %>%
  melt(id = c("year", "Breaks"), variable.name = "parameter") %>%
  ggplot(aes(x = year, y = value)) + 
    geom_line(aes(x = year, y = value, linetype = parameter, color = Breaks)) +
    scale_color_brewer(palette = "Purples") +
  theme(panel.border = element_blank(),
          panel.grid.major = element_blank(),
          panel.grid.minor = element_blank(),
          panel.background = element_rect(fill = "#fafafa"),
          plot.background = element_rect(fill = "white")
        )
```

```{r}
mtr %>%
  mutate(Breaks = as.factor(Breaks)) %>%
  ggplot(aes(x = year, y = parameter_k, color = Breaks)) + 
    geom_point() + 
    geom_line() + 
    scale_color_brewer(palette = "Blues") +
  theme(panel.border = element_blank(),
          panel.grid.major = element_blank(),
          panel.grid.minor = element_blank(),
          panel.background = element_rect(fill = "#fafafa"),
          plot.background = element_rect(fill = "white")
        )
```

calculate different

```{r}
list <- c()
listB <- c()
Year <- c()
dlist <- c()
elist <- c()
for(n in BREAKS){
  for(i in YEAR){
    data %>%
      filter((year >= i) & (year <= i + 9)) %>%
      pull(prcp) %>%
      hist(breaks = n, plot = FALSE) -> hist
    hist$counts %>% sum() -> sum
    x <- hist$mids 
    y <- hist$counts/sum 
    data.frame(x, y) -> dens 
    mod <- drm(data = dens, y ~ log(x), fct = EXD.2())
    d <- mod$parmMat[1]
    e <- mod$parmMat[2]
    k <- 1/e/d
    p <- 1 - pexp(log(600)*k, d)
    list <- c(list, p)
    listB <- c(listB, n)
    Year <- c(Year, i)
    dlist <- c(dlist, d)
    elist <- c(elist, e)
  }}
mtr <- data.frame(year = Year,
                    Breaks = listB, 
                      Probability = list, 
                  parameter_d = dlist,
                  parameter_e = elist)

```

```{r}
mtr %>%
  mutate(Breaks = as.factor(Breaks)) %>%
  ggplot(aes(x = year, y = Probability, color = Breaks)) + 
    geom_point() + 
    geom_line() + 
    scale_color_brewer(palette = "Blues") +
  theme(panel.border = element_blank(),
          panel.grid.major = element_blank(),
          panel.grid.minor = element_blank(),
          panel.background = element_rect(fill = "#fafafa"),
          plot.background = element_rect(fill = "white")
        )
```

```{r}
g <- df %>%
  ggplot(aes(x = date, y = prcp)) + 
  geom_line(color = "blue") + 
  theme(panel.border = element_blank(),
          panel.grid.major = element_blank(),
          panel.grid.minor = element_blank(),
          panel.background = element_rect(fill = "#fafafa"),
          plot.background = element_rect(fill = "white")
        ) + 
  geom_line(aes(x = date, y = rep(1500, length(date))), color = "lightblue") + 
  ylab("Precipitation (in tenth of mm")
ggplotly(g)
```

```{r}
data %>%
  filter(prcp >= 1000)
```

```{r}
mtr %>%
  filter(Breaks == 21) %>%
  left_join(meth, by = c("year" = "Year")) %>%
  select(year, Probability, Length) %>%
  mutate(days = Probability*Length)
```
